Jonathan Majors called 911 on behalf of his accuser, Grace Jabbari, the day he was arrested -- and now, we know what he officially reported it as ... a possible overdose, suicide.

Two NYPD officers who responded to the scene back in March took the stand Tuesday in Majors' assault trial, and their testimony was interesting ... mostly 'cause they gave the blow-by-blow (or as much as they could recall, anyway) from the moment they arrived.

One of the cops testified the initial call that came in -- made by Majors himself -- was to report someone who'd attempted to take their own life via overdose.

The cops also noted when they got there, Jabbari was on the floor in Majors' apartment ... and that when she finally awoke, the first thing she asked was how she'd gotten there. They also testified that Jabbari then asked if Majors was there or if he was outside, seemingly worried.

Another interesting tidbit ... the officers testified that Jabbari asked them why her ear had hurt -- remember, a cut ear is one of the reasons Majors is being prosecuted -- but, on the stand, the officers conceded they did not ask her if she'd fallen.

As for what Jabbari did say about injuries ... they testified she said Majors had hit her several times in the head, and that he'd grabbed her by the throat.

One of the officers also admitted on the stand he'd helped Jabbari fill out her DV report ... completing page 1 for her, and letting her do page 2 on her own. On cross, the officers said they didn't recall a lot of specific details that Majors' defense team asked ... including whether Jabbari had told them she'd taken 2 sleeping pills earlier in the night.

Last thing ... the officers said they noted a button on Majors' coat appeared to be missing, and they also said they noticed a small amount of blood on Majors' comforter on his bed when they arrived -- but didn't see any other signs of blood.